Solving the pooling problem with LMI relaxations

We consider the standard pooling problem with a single quality parameter, which is a polynomial global optimization problem occurring among other places in the oil industry. In this paper, we show that if the feasible set has a nonempty interior, the problem can be solved by a hierarchy of semidefinite relaxations in which the resulting sequences of their optimal values converge to the global optimum. For a fixed relaxation order, this technique provides tight lower bounds for the global objective function value. Based on the experiments, for low order relaxations, the lower bound provided by this method matches the true global optimum in several instances